Pitch Black (which launched Vin Diesel’s career) feels like an Alien movie because, immediately prior to making it, director David Twoy pitched to make Alien 3, then made a few tweaks to his rejected script.
I have read elsewhere (can’t find it now) that many twin films start out as the same film, but then the team splits over creative differences and one half makes one film and the other half makes its sibling.
You’re right about the competition thing: for 1974’s Towering Inferno, producers hedged their bets against copycat disaster flicks by pooling resources with other studios to make one all-star blockbuster.
Then you get into really weird territory with Disney’s Pirates of the Caribbean. The theme park ride inspired the Monkey Island video games, which were also loosely based on a novel called On Stranger Tides.
Monkey Island was to be adapted into a film written by Ted Elliott, which was cancelled, but he then adapted those scripts into the first two Pirates of the Caribbean films (which were based on Disney’s theme park ride and Monkey Island). However, Ted Elliott hadn’t actually read On Stranger Tides until production of the third Pirates film.
Pirates of the Caribbean: On Stranger Tides became the fourth film in the franchise, making it the first proper film adaptation of the novel, but the fourth in a franchise based on the same novel and a video game based also on the same novel, of which the video game was based on the same theme park ride as all the films. Phew!